Try to describe the Ex and you have a problem. The Dutch band may have celebrated their 30th birthday recently, but you would try to sum up their sound in two or three words at your peril. This is a ­quandary shared by the band members themselves. I meet them in Dublin, where they are playing a one-off date. The cab driver ­taking them to the venue asked them what they sound like. "We had real difficulty," says Andy Moor, the band's London-born guitarist, who boasts 15 years' service. "It is really hard!" "We feel a bit stupid as it can sound very ­pretentious, 'We are very unique, we are not like ­anyone else,'" says Terrie Hessels, the only remaining member of the band's original 1979 lineup.

Yet unique is what the Ex are. Take any major musical development of the last 50 years and you can almost guarantee that they have either incorporated it into their sound or played with it and discarded it. Their recent retrospective CD 30 contains a dazzling array of sounds that range from industrial to orchestral. Though the band's real move forward, and one which brought them to the attention of the jazz world, was their 1991 collaboration with (now sadly deceased) US cellist Tom Cora. This lead to further unions, with the likes of zany Dutch jazz drummer Han Bennink as well as English saxophonist John Butcher.

Even now, the kind of phrases used on gig posters and in the music press range from "anarcho-punk" to "improvised jazz" to "afro-punk" and "folk". The punk part may be fair – the band certainly formed with that ethos and a staccato approximation of the sound of the Fall or Gang of Four, but they have always been far more experimental than their three-chord forebears.

They chose their name for the ease with which it could be sprayed on walls, and drew straws to decide who would play what. There was always an exploratory and political edge to the band, as evidenced by the 1983 concept set of four 7in singles about a closed factory in the Amsterdam suburb of Wormer where the band formed. Since then, the Ex have taken in folk influences from all over Europe. They have dabbled in jazz, improvisation, guitar ­destruction, drilling venue walls, dance music, ­military-band precision, ska, toy instruments, horns, African beats and sampling. I could go on. Yet, surprisingly, none of this comes across as radical departure in style. They still sound like the Ex on every recording and at every gig. The guitars retain a caustic, rhythmic precision and the drumming is tight and complex.

"One reason we are hard to describe is that we never had an education at music school, and in that sense we are not ­influenced by any traditional playing," says Katherina Bornefeld, neatly sidestepping any attempt to form a soundbite encapsulating the Ex's sound, despite her 25 years on the drum stool.

In order to understand the band you need to see them perform; they work in the opposite manner to most groups. The Ex write songs to perform live, tweaking them as tours progress and then recording the honed versions as documents of their time. Most Ex tours start with an entire batch of new material – there is no roster of crowd-pleasers to get the audience going. The dedicated fan is as challenged as someone hearing the band for the very first time.

This is a band very much about intuition. Moor plays intricate notes on a ­baritone guitar with his eyes closed before dashing at Hessels, both raising their ­guitars as the newest member of the band, Arnold de Boer (who last year replaced founder-member GW Sok), ducks beneath them. Meanwhile, Bornefeld seemingly hits every piece of her drumkit, before repeating the rhythm in a slightly different ­pattern. Moor aims kicks at the air – band members even try to put each other off at times. The band have a reputation for addressing serious politics, but they also have a great sense of humour. This is neatly evidenced by the 7in singles club they ran for a year, where the last single was a 12in and thus could not be squeezed into the box that came with the first record in the series.

As well as being a drumming original, Bornefeld also possesses a voice made for singing folk music in any language, which has come to the fore on the band's tours of Ethiopia. Born out of sheer enthusiasm for the music and people of the country, the Ex's Ethiopian tours ­took loud ­guitar music where it has never been before, as well as exchanging ideas and technical know-how with local musicians. They also played with Ethiopian saxophone legend Getatchew Mekurya, and collaborated with him on an album.

"There is no tour circuit," says Hessels. "We even went to places that hardly any Ethiopian ­musicians had played."

"One time we were playing in a barn on a farm and another time in the police community hall," adds Moor. "We would just go to the chief of the town and they decided what we should pay, sometimes it was $20 and sometimes it was free."

The band took generators and ­amplifiers with them, and left them behind for local musicians to use. They follow a ­similar DIY philosophy with all their work. The band has no manager, driver or roadies and they put out all their CDs themselves. Yet they also find time to have countless side projects, such as Bornefeld's ­KatJonBand with the Mekons' Jon Langford, Moor's solo album and ­Hessels's work with Sonic Youth's Thurston Moore.

Their free gigs in Ethiopia, which attracted crowds of 2,000 or more, have also left what could be a strange musical legacy. If ­Ethiopia starts throwing up scratchy, indefinable guitar bands, you'll know who to blame. "Everyone still uses cassettes there," says Moor. "We went back to pressing up cassettes, giving them out to taxi drivers all over the place. So at least they know what we sound like."

An initial pressing of 10,000 cassettes, with more to follow and the inevitable home-taping, have made the Ex established favourites in parts of Ethiopia, but in the UK they remain something of a word-of-mouth aural delicacy. Their arrival on these shores for their first tour since 2003 should help to remedy that, especially as they have integrated yet more new sounds in the shape of Brass Unbound, a four-piece horn section of prodigious talents.

With this addition to their ranks, the Ex once again deter any attempts at description. But you get the feeling that as soon as anyone nailed their sound, the band would do their damnedest to defy it.

The Ex play the Fleece, Bristol on 29 January, then touring. Details: theex.nl